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Algebraic and Geometric Topology http://dx.doi.org/10.1090/pspum/032.2 PROCEEDINGS OF SYMPOSIA IN PURE MATHEMATICS Volume XXXII, Part 2 ALGEBRAIC AND GEOMETRIC TOPOLOGY AMERICAN MATHEMATICAL SOCIETY PROVIDENCE, RHODE ISLAND 1978 PROCEEDINGS OF THE SYMPOSIUM IN PURE MATHEMATICS OF THE AMERICAN MATHEMATICAL SOCIETY HELD AT STANFORD UNIVERSITY STANFORD, CALIFORNIA AUGUST 2-21, 1976 EDITED BY R. JAMES MILGRAM Prepared by the American Mathematical Society with partial support from National Science Foundation grant MCS 76-01696 Library of Congress Cataloging in Publication Data Symposium in Pure Mathematics, Stanford University, 1976. Algebraic and geometric topology. (Proceedings of symposia in pure mathematics; v. 32) "Proceedings of the Symposium in Pure Mathematics of the American Mathema• tical Society, held at Stanford University, Stanford, California, August 2—21, 1976." Bibliography: v. 1, p. v. 2, p. 1. Algebraic topology—Congresses. 2. Manifolds (Mathematics)—Congresses. 3. Global analysis (Mathematics)—Congresses. I. Milgram, R. James. II. American Mathematical Society. III. Title. IV. Series. QA612.S93 1976 514'.2 78-14304 ISBN 0-8218-1432-X (v. 1) ISBN 0-8218-1433-8 (v. 2) COPYING AND REPRINTING. Individual readers of this publication, and nonprofit li• braries acting for them, are permitted to make fair use of the material, such as to copy an article for use in teaching or research. Permission is granted to quote brief passages from this publication in reviews, provided the customary acknowledgment of the source is given. Republication, systematic copying, or multiple reproduction of any material in this publi• cation (including abstracts) is permitted only under license from the American Mathematical Society. Requests for such permission should be addressed to the Executive Director, American Mathematical Society, P.O. Box 6248, Providence, Rhode Island 02940. The appearance of the code on the first page of an article in this book indicates the copyright owner's consent for copying beyond that permitted by Sections 107 or 108 of the U.S. Copyright Law, provided that the fee of $1.00 plus $.25 per page for each copy be paid directly to the Copyright Clearance Center, Inc., 21 Congress Street, Salem, Massachusetts 01970. This consent does not extend to other kinds of copying, such as copying for general distribution, for advertising or promotional purposes, for creating new collective works, or for resale. AMS (MOS) subject classifications (1970). Primary 53C15, 53C30, 53C35, 53C40, 55-XX, 57Axx, 57Bxx, 57Cxx, 57Dxx, 58Bxx, 58C25, 58Dxx, 58Gxx. Copyright © 1978 by the American Mathematical Society Reprinted 1989 Printed in the United States of America All rights reserved except those granted to the United States Government. This book may not be reproduced in any form without permission of the publishers. The paper used in this book is acid-free and falls within the guidelines established to ensure permanence and durability. © PREFACE The American Mathematical Society held its 24th Summer Research Institute at Stanford University from August 2-21, 1976. The topic of the meeting was Alge• braic and Geometric Topology. Particular emphasis was placed on Algebraic K- and L-Theory, Surgery and Surgery Classifying Spaces, Group Actions on Mani• folds, and 3 and 4 Manifold Theory. The organizing committee consisted of Raoul Bott, William Browder (Co- chairman), Pierre Conner, Robion Kirby, Richard Lashof, R. James Milgram (Chairman), Daniel Quillen, and P. Emery Thomas (Co-chairman). The main lecturers were Raoul Bott, Richard Lashof and Mel Rothenberg, Syl- vain Cappell and Julius Shaneson, C. McA. Gordon, Robert Edwards, Allen Hatcher and Jack Wagoner, Wu. C. Hsiang, Max Karoubi, R. James Milgram, Daniel Quillen, Laurence Siebenmann, and C. T. C. Wall. Special hour lectures were given by Gregory Brumfiel, William Jaco, Robion Kirby, Ronnie Lee, James Lin, lb Madsen, John Morgan, Robert Oliver, Ted Petrie, P. Emery Thomas, F. Waldhausen, and James West. There was also a series of problem sessions run by Raoul Bott (foliations), W. C. Hsiang (group actions and surgery), R. Kirby (3 and 4 manifolds), and C. T. C. Wall (algebraic K- and £-theory). Among the more active seminars were 3 and 4 manifolds (Kirby), Kervaire in• variant (Browder—E. Brown), Homotopy theory (E. Thomas—M. Mahowald), Algebraic K- and L- theory (J. Wagoner), Group actions (W. C. Hsiang), Folia• tions (Bott), Geometry of manifolds (L. Siebenmann), and Surgery and surgery classifying spaces (R. Lashof). These proceedings include write ups of most of the main lectures, as well as selected seminar talks, and most of the problem sessions. The institute was sponsored by the National Science Foundation under contract number MCS 76-01696. The organizing committee wishes to thank Dorothy Smith of the American Mathematical Society for her help in running and organizing the conference. R. JAMES MILGRAM STANFORD UNIVERSITY ni TABLE OF CONTENTS Structure of Topological Manifolds TAKAO MATUMOTO, Triangulation of manifolds 3 DAVID E. GALEWSKI AND RONALD J. STERN, Simpiicial triangulations of topological manifolds 7 ALLAN L. EDMONDS, Fibering topological manifolds ..13 Low Dimensional Manifolds FRIEDHELM WALDHAUSEN, Recent results on sufficiently large 3-manifolds 21 A. J. CASSON AND C. MCA. GORDON, On slice knots in dimension three 39 JOHN R. STALLINGS, Constructions of fibred knots and links ...55 HUGH M. HILDEN AND JOSE M. MONTESINOS, A method of constructing 3-manifolds and its application to the computation of the /^-invariant 61 WILLIAM JACO AND PETER B. SHALEN, A new decomposition theorem for irreducible sufficiently-large 3-manifolds 71 MICHAEL FREEDMAN AND ROBION KIRBY, A geometric proof of Rochlin's theorem .85 YUKIO MATSUMOTO, Secondary intersectional properties of 4-manifolds and Whitney's trick ...99 Geometry of Differential Manifolds and Algebraic Varieties E. REES AND E. THOMAS, Smoothings of isolated singularities ....Ill JOHN O. MORGAN, Hodge theory for the algebraic topology of smooth algebraic varieties ....119 SYLVAIN E. CAPPELL AND JULIUS L. SHANESON, An introduction to embeddings, immersions and singularities in codimension two 129 DONALD DAVIS AND MARK MAHOWALD, Immersions of projective spaces 151 WILLIAM D. HOMER, Singularities in lens spaces ..155 FRANZ W. KAMBER AND PHILIPPE TONDEUR, Characteristic classes and Koszul complexes ....159 WENSOR LING, Translations on M x R ... 167 WALTER D. NEUMANN, Homotopy invariance of Atiyah invariants .....181 HERBERT SHULMAN, Covering dimension and characteristic classes for foliations 189 JOHN W. WOOD, A connected sum decomposition for complete intersections 191 STEPHEN SHING-TOUNG YAU, Normal singularities of surfaces. 195 v VI TABLE OF CONTENTS //-Spaces, Loop Spaces, and CW Complexes JAMES P. LIN, On the topology of finite /f~spaces 201 JOHN R. HARPER, On the construction of mod p /2-spaces 207 ERIK KJAER PEDERSEN, Smoothings of ff-spaees 215 PETER J. KAHN, The homotopy-dimension of nilpotent spaces 217 JOEL M. COHEN, Complexes of cohomological dimension two. 221 F. R. COHEN, M. E. MAHOWALD AND R. J. MILGRAM, The stable decomposition for the double loop space of a sphere 225 J. P. MAY, H^ ring spectra and their applications .....229 F. R. COHEN, Little cubes and the classifying space for w-sphere fibrations ...245 Problems W. BROWDER AND W. C. HSIANG, Some problems on homotopy theory, manifolds and transformation groups .251 COMPILED BY MARK MOSTOW AND PAUL SCHWEITZER, Foliation problem session (R. Bott)..... 269 ROB KIRBY, Problems in low dimensional manifold theory 273 FRIEDHELM WALDHAUSEN, Some problems on 3-manifolds 313 .
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